Problem: Simplify the following expression and state the condition under which the simplification is valid: $r = \dfrac{a^2 + a}{a^2 - 3a - 4}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{a^2 + a}{a^2 - 3a - 4} = \dfrac{(a)(a + 1)}{(a - 4)(a + 1)} $ Notice that the term $(a + 1)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(a + 1)$ gives: $r = \dfrac{a}{a - 4}$ Since we divided by $(a + 1)$, $a \neq -1$. $r = \dfrac{a}{a - 4}; \space a \neq -1$